Continual Learning (CL) methods aim to learn from a sequence of tasks while avoiding the challenge of forgetting previous knowledge. We present DREAM-CL, a novel CL method for ECG arrhythmia detection that introduces dynamic prototype rehearsal memory. DREAM-CL selects representative prototypes by clustering data based on learning behavior during each training session. Within each cluster, we apply a smooth sorting operation that ranks samples by training difficulty, compressing extreme values and removing outliers. The more challenging samples are then chosen as prototypes for the rehearsal memory, ensuring effective knowledge retention across sessions. We evaluate our method on time-incremental, class-incremental, and lead-incremental scenarios using two widely used ECG arrhythmia datasets, Chapman and PTB-XL. The results demonstrate that DREAM-CL outperforms the state-of-the-art in CL for ECG arrhythmia detection. Detailed ablation and sensitivity studies are performed to validate the different design choices of our method.